An approach for code generation in the Sparse Polyhedral Framework

Strout, Michelle Mills; LaMielle, Alan; Carter, Larry; Ferrante, Jeanne; Kreaseck, Barbara; Olschanowsky, Catherine

doi:10.1016/j.parco.2016.02.004

Cited by 31 publications

(12 citation statements)

References 68 publications

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“…Tiling of consecutive SpMVs on unstructured grids is much harder. However, the sparse polyhedral framework (SPF) [35,25], an extension of full sparse tiling [34], attempts to generalize polyhedral loop transformations to codes with indirect memory references, as used in general SpMVs. While the standard polyhedral framework is restricted to compiling c 2015 U.S. Government Downloaded 07/18/15 to 130.132.123.28.…”

Section: Discussionmentioning

confidence: 99%

Modeling the Performance of Geometric Multigrid Stencils on Multicore Computer Architectures

Ghysels¹,

Vanroose²

2015

SIAM J. Sci. Comput.

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The basic building blocks of the classic geometric multigrid algorithm all have a low ratio of executed floating point operations per byte fetched from memory. On modern computer architectures, such computational kernels are typically bound by memory traffic and achieve only a small percentage of the theoretical peak floating point performance of the underlying hardware. We suggest the use of state-of-the-art (stencil) compiler techniques to improve the flop per byte ratio, also called the arithmetic intensity, of the steps in the algorithm. Our focus will be on the smoother which is a repeated stencil application. With a tiling approach based on the polyhedral loop optimization framework, data reuse in the smoother can be improved, leading to a higher effective arithmetic intensity. For an academic constant coefficient Poisson problem, we present a performance model for the multigrid V -cycle solver based on the tiled smoother. For increasing numbers of smoothing steps, there is a trade-off between the improved efficiency due to better data reuse and the additional flops required for extra smoothing steps. Our performance model predicts time to solution by linking convergence rate to arithmetic intensity via the roofline model. We show results for two-dimensional (2D) and three-dimensional (3D) simulations on Intel Sandy Bridge and for 2D simulations on Intel Xeon Phi architectures. The actual performance is compared with the theoretical predictions.

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Section: Discussionmentioning

confidence: 99%

Modeling the Performance of Geometric Multigrid Stencils on Multicore Computer Architectures

Ghysels¹,

Vanroose²

2015

SIAM J. Sci. Comput.

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“…As mentioned above, these approaches focus on dense loops over dense arrays, so are not applicable to our domain. There has been work done in the past to generalize the loop-based model to handle non-affine loop bounds and subscripts using symbolic expressions [23,34], and to handle sparse matrices and arrays [30][31][32]35], but these approaches still only target loops, and hence do not generalize to the recursive constructs we consider. To break down the transformations a little more concretely, first, the method outer was strip mined (Section 5.3.4) to break it into two loops, outer1 (at line 1) and outer2 (at line 16); outer2 performs groups of 4 iterations from outer1.…”

Section: Other Related Workmentioning

confidence: 99%

Composable, sound transformations of nested recursion and loops

Sundararajah

Kulkarni

2019

Proceedings of the 40th ACM SIGPLAN Conference on Programming Language Design and Implementation

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Scheduling transformations reorder a program's operations to improve locality and/or parallelism. The polyhedral model is a general framework for composing and applying instancewise scheduling transformations for loop-based programs, but there is no analogous framework for recursive programs. This paper presents an approach for composing and applying scheduling transformations-like inlining, interchange, and code motion-to nested recursive programs. This paper describes the phases of the approach-representing dynamic instances, composing and applying transformations, reasoning about correctness-and shows that these techniques can verify the soundness of composed transformations.

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“…Strout et al [56] first demonstrated the feasibility of automatically generating inspectors and composing separately specified inspectors using the sparse polyhedral framework; the inspector-executor generator prototype composed inspectors by representing them using a data structure called an inspector dependence graph. Subsequently, Venkat et al [29], [57] developed automatically-generated inspectors for nonaffine transformations and for data transformations to reorganize sparse matrices into different representations that exploit the structure of their nonzeros.…”

Section: Polyhedral Compiler Optimization Of Sparse Matricesmentioning

confidence: 99%

Automating Wavefront Parallelization for Sparse Matrix Computations

Venkat¹,

Mohammadi²,

Park³

et al. 2016

SC16: International Conference for High Performance Computing, Networking, Storage and Analysis

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This paper presents a compiler and runtime framework for parallelizing sparse matrix computations that have loopcarried dependences. Our approach automatically generates a runtime inspector to collect data dependence information and achieves wavefront parallelization of the computation, where iterations within a wavefront execute in parallel, and synchronization is required across wavefronts. A key contribution of this paper involves dependence simplification, which reduces the time and space overhead of the inspector. This is implemented within a polyhedral compiler framework, extended for sparse matrix codes. Results demonstrate the feasibility of using automaticallygenerated inspectors and executors to optimize ILU factorization and symmetric Gauss-Seidel relaxations, which are part of the Preconditioned Conjugate Gradient (PCG) computation. Our implementation achieves a median speedup of 2.97× on 12 cores over the reference sequential PCG implementation, significantly outperforms PCG parallelized using Intel's Math Kernel Library (MKL), and is within 6% of the median performance of manually-parallelized PCG.

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An approach for code generation in the Sparse Polyhedral Framework

Cited by 31 publications

References 68 publications

Modeling the Performance of Geometric Multigrid Stencils on Multicore Computer Architectures

Modeling the Performance of Geometric Multigrid Stencils on Multicore Computer Architectures

Composable, sound transformations of nested recursion and loops

Automating Wavefront Parallelization for Sparse Matrix Computations

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